This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A319088 #15 Feb 16 2025 08:33:56
%S A319088 1,13,40,136,211,535,682,1322,1808,2708,3071,5663,6170,7934,9959,
%T A319088 13799,14666,20498,21581,28781,32750,37106,38693,55973,59723,65807,
%U A319088 73097,87209,89732,114032,116915,138419,148220,158624,169649,216305,220412,233408,247097
%N A319088 a(n) = Sum_{k=1..n} k^2*tau_3(k), where tau_3 is A007425.
%H A319088 G. C. Greubel, <a href="/A319088/b319088.txt">Table of n, a(n) for n = 1..10000</a>
%H A319088 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StieltjesConstants.html">Stieltjes Constants</a>
%H A319088 Wikipedia, <a href="http://en.wikipedia.org/wiki/Stieltjes_constants">Stieltjes constants</a>
%F A319088 a(n) ~ n^3 * (log(n)^2/6 + (gamma - 1/9)*log(n) + gamma^2 - gamma/3 - g1 + 1/27), where gamma is the Euler-Mascheroni constant A001620 and g1 is the first Stieltjes constant A082633.
%t A319088 nmax = 50; Accumulate[Table[k^2*Sum[DivisorSigma[0, d], {d, Divisors[k]}], {k, 1, nmax}]]
%o A319088 (PARI) tau_3(k) = vecprod(apply(e -> (e+1)*(e+2)/2, factor(k)[, 2]));
%o A319088 a(n) = sum(k = 1, n, k^2 * tau_3(k)); \\ _Amiram Eldar_, Jan 18 2025
%Y A319088 Cf. A007425, A061201, A318750.
%Y A319088 Cf. A001620, A082633.
%K A319088 nonn
%O A319088 1,2
%A A319088 _Vaclav Kotesovec_, Sep 10 2018